Procedural Snow with Particles
I've only a week ago done a basic but effective looking snowfall. I'll try and place the Blender file up here.  I used two emitters, one for distant flakes and another for closer and a circular variety.  The Blender file  (just over 3 MB)...



As for directional flow, go to the emitter's "Velocity" tab and drag X, Y or Z values to suit.  You can also turn gravity off if desired.  You'll find that under the "Field Weights" tab further down.

As snowflakes can flutter on the way down, I've adjusted the Brownian value in the "Physics" tab.

Apologise for the missing texture files - tried to pack them into the Blender file but it kept coming up with "cannot find errors" even when I moved the files into the project's folder and re-saved.

Everything you need is still there and the snow still works though. (CTL-A)

Screenshot -